Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main{

    public static void main(String[] args) throws IOException {
        
       BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
       
       int n = Integer.parseInt(br.readLine());
       double t,x;
       n = n*2;
       int v = (int)Math.round(Math.sqrt(n));
       boolean f = false;
       
        for (int i = 1; i < v; i++) {
             x=n - i * i - i;
             t = Math.floor(Math.sqrt(x));
             if(t*(t+1)==x){
             f=true;
             break;
             }
        }
        
        if(f){
            System.out.println("YES");
        }else{
            System.out.println("NO");
        }
    }
}